The black hole information problem beyond quantum theory

Abstract

The origin of black hole entropy and the black hole information problem provide important clues for trying to piece together a quantum theory of gravity. Thus far, discussions on this topic have mostly assumed that in a consistent theory of gravity and quantum mechanics, quantum theory will be unmodified. Here, we examine the black hole information problem in the context of generalisations of quantum theory. In particular, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We compute the time it takes information to escape a black hole, assuming that information is preserved. We find that under some very general assumptions, the arguments of Page (that information should escape the black hole after half the Hawking photons have been emitted), and the black-hole mirror result of Hayden and Preskill (that information can escape quickly) need to be modified. The modification is determined entirely by what we call the Wootters-Hardy parameter associated with a theory. We find that although the information leaves the black hole after enough photons have been emitted, it is fairly generic that it fails to appear outside the black hole at this point -- something impossible in quantum theory due to the no-hiding theorem. The information is neither inside the black hole, nor outside it, but is delocalised. Our central technical result is an information decoupling theorem which holds in the generalised probabilistic framework.

12 pages + appendix, 5 figures. Comments welcome. v2: typos corrected, published version

References in corpus (14)

• Black holes as mirrors: quantum information in random subsystems
• Information in Black Hole Radiation
• Fast Scramblers
• A generalized no-broadcasting theorem
• Quantum state merging and negative information
• The mother of all protocols: Restructuring quantum information's family tree
• Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox
• Entropy and Information Causality in General Probabilistic Theories
• Entropy in general physical theories
• Hawking Radiation and Back-Reaction
• The structure of reversible computation determines the self-duality of quantum theory
• Information locking in black holes
• Unifying typical entanglement and coin tossing: on randomization in probabilistic theories
• Black hole evaporation rates without spacetime

Cited by in corpus (6)

• Time Dependence of Hawking Radiation Entropy
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Quantum from principles
• Quasi-quantization: classical statistical theories with an epistemic restriction
• The completeness of quantum theory for predicting measurement outcomes
• Entropy, majorization and thermodynamics in general probabilistic theories